Calculate the 68-95-99.7 Rule with Interactive Visualization
Use our free empirical rule calculator to find percentages within 1, 2, and 3 standard deviations of the mean in a normal distribution.
The Empirical Rule, also known as the 68-95-99.7 rule or three-sigma rule, is a statistical principle that describes how data is distributed in a normal distribution (bell curve).
This rule states that for a normal distribution:
This calculator provides instant results and visual representation to help you understand how your data is distributed according to the empirical rule.
Advanced calculator featuring interactive graphs and detailed visual representations of the normal distribution curve.
Open ToolStep-by-step instructions and simulation for calculating empirical rule using TI-84 calculator functions.
Open ToolCalculate specific ranges and percentages for any interval within the normal distribution curve.
Open ToolExcel formulas and templates for calculating empirical rule with downloadable spreadsheets.
Open ToolDetailed step-by-step solutions showing how to calculate empirical rule manually with explanations.
Open ToolCalculate empirical rule considering sample size effects and confidence intervals for statistical analysis.
Open ToolThe Empirical Rule applies to datasets that follow a normal distribution (bell-shaped curve). It's most accurate when your data is symmetric and follows the standard normal distribution pattern.
If your data doesn't follow a normal distribution, the Empirical Rule may not be accurate. In such cases, consider using Chebyshev's theorem or other statistical methods appropriate for your data distribution.
For perfectly normal distributions, the rule is exact. For real-world data that approximates normal distribution, it provides a very good approximation, typically within 1-2% of the actual values.